Modélisation déterministe de la crue extrême d'un bassin versant de montagne avec application de la description géomorphologique du réseau hydrographique eterministic extreme flood modelling of a mountainous catchment with use of a geomorphologic description of the channel network

Résumé

Les méthodes de calcul des crues de projet pour des grands barrages sont de type statistique ou de type déterministe (PMP/PMF). Ce dernier type de méthodes est principalement utilisé dans le monde anglo-saxon (États-Unis, Australie), mais peut offrir une alternative intéressante aux méthodes statistiques, qui présentent des lacunes pouvant être importantes.

Une application des méthodes PMP/PMF sur des bassins suisses a mis en évidence l'intérêt de ces méthodes, mais aussi leurs faiblesses. Une adaptation des outils déterministes est nécessaire pour prendre en compte les particularités des bassins de montagne. Il s'agit principalement de mieux tenir compte des propriétés physiques des bassins versants et des phénomènes de non linéarité.

Dans ce but, un concept de modélisation utilisant la description géomorphologique du bassin versant a été utilisé et amélioré.

Le premier modèle utilisé est l'hydrogramme unitaire géomorphologique, qui existe depuis 1979. Le deuxième modèle utilise le concept de cascade de réservoirs hydrologiques à vidange non linéaire, dont les éléments sont issus de la description géomorphologique du bassin. C'est là une modélisation nouvelle qui est particulièrement adaptée au contexte des crues extrêmes dans les Alpes. Un travail de calibration et validation du modèle a montré que ce modèle a un bon potentiel d'utilisation. La principale difficulté revient à identifier la signification physique des paramètres du modèle, qui pourrait s'appuyer sur les résultats d'un autre type de modélisation couplant la géomorphologie du bassin aux equations de l'onde cinématique. Ce modèle est en cours de test à l'IATE.

Mots-clés:

• Crue extrême,
• bassin versant de montagne,
• méthodes PMP/PMF,
• modèles déterministes,
• description géomorphologique du bassin versant

Abstract

Design floods for large dams are computed either with statistical or deterministic methods (Probable maximum precipitation, PMP/probable maximum flood, PMF). The latter presents an interesting alternative to statistical rnethods, whose drawbacks may be significant, especially when hydrometeorological data are deficient.

PMP/PMF methods are based on assumption of the existence of an upper limit of the hydrometeorological processes. The prevalent method for PMP estimation is the maximization - transposition technique. Simpler methods, such as the statististically based technique, also exist. However, the most accurate method may well be the use of a meteorological model, but this aspect is still in the research domain.

PMF is derived from a PMP using a simplified loss function and a transfer function for which parameters are maximized. The prevalent transfer function is the unit hydrograph model.

Application of traditional PMP/PMF method on alpine catchments showed important weaknesses due to the transfer function. Alpine catchments are characterized by steep slopes, thin soil cover, poor vegetation, and large floods are due to heavy, short thunderstorms. Consequently, hydrological response is very sensitive to the topography of the catchment. Nonlinearity must be taken into account in many cases. However, experience showed that a model cannot take into account a detailed description of the catchment.

In order to take into account the characteristcs of alpine catchments while staying as simple as possible, we have used the geomorphologic description of the catchment as a modeling basis. This representation is based on the Strahler ordering scheme, and defines all possible path types that a surface runoff dropret may follow to reach the outlet. This description has been used since 1979 in the geomorphologic unit hydrograph (GUH) formulation.

We developed a geomorphorogic nonlinear cascade (GNC) in order to take into account nonlinear processes. The GNC model uses the geomorphologic description of the catchment to define the reservoirs of hydrological cascades. A cascade represents a path type; the first reservoir ofa cascade is an overland element and subsequent reservoirs are channels with increasing Strahler's order. Outflow from a reservoir is the inflow of the downstream reservoir. Outflows from all cascades are combined to produce the global catchment response. The two equations used in the GNC model are a global continuity equation: I - O = dV/dt, and a nonlinear outflow equation: O = k V^x, where I is an input term, that is precipitation for the first reservoir, and outflow from the upstream element for channel reservoirs, V is the volume of water stored in a reservoir at time t, k is a consfant, and x an exponent. The parameter k varies with each reservoir as a function of surface area (for overland erements) or rength (for channel elements). The exponent x should be between 1 and 2.

The two models, GUH and GNC, have been calibrated with an automatic optimization procedure, and tested on the Vogelbach catchment. This catchment is located in the swiss alps (Arptar, canton of schwytz); it is a third order catchment, and its area is 1,55 km². Both models gave good results, although the GUH model had a tendency to smooth the dischage.

Inorder to improve the physical meaning of the moder parameters, we are testing a third model linking the geomorphologic description with the kinematic wave equations. Results are promising, but are not shorm in this paper.

The hydrologic modeling based on the geomorphologic description of the catchment seems to be a good compromise between lumped modeb and detailed distributed models, which are difficult to apply.

Keywords:

• Extreme flood,
• mountainous catchment,
• PMP/PMF,
• deterministic model,
• geomorphologic descritption of catchment